Cluster Scatterings and Spectra. I. Electrons in Substitutional Alloys

A diagrammatical analysis of a previously reported set of approximations for the averaged electronic resolvent 〈[z ‐ H ] −1 〉 in substitutional alloys is made. The results are found to be in correspondence with applicability of the method revealed in a numerical analysis beyond the coherent potential approximation. A new modification of the method is suggested which is free of shortcomings of the original version. It enables relatively very easy and in principle almost exact computer calculations of spectra of substitutional alloys, at least for simplest model Hamiltonians. A simple numerical example is solved.